Regular rotating electrically charged black holes and solitons in non-linear electrodynamics minimally coupled to gravity

In non-linear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have an obligatory de Sitter center. By the Gurses-Gursey algorithm they are transformed to spinning electrically charged solutions that are asymptotically Kerr-Newman for a distant observer. Rotation transforms the de Sitter center into a de Sitter vacuum surface which contains the equatorial disk r = 0 as a bridge. We present a general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.